Smoothing and differentiating circuit



Dec. 27, 1949 D. J. CAMPBELL ET AL SMOOTHING AND DIFFERENTIATING CIRCUITe sheets-sheet 1 Filed Dec. 30, 1942 INVENTORS.'

D. J. CAMPBELL BY w. G. WING ATTORNEY- Dec. 27, 1949 D. J. CAMPBELL. ErA1. i 2,492,355

SMOOTHING AND DIFFERENTIATING CIRCUIT Filed Dec. 30, .1 942 6Sheets-Sheet 2 n R 7'0 67 MULT. l l sm A 55 A Ao le] INE g o uNl-r -65-xo '03,22% cos Ao 1 59/ R MuLt 7l) (o uNn' 1T es y0 RECTILlNEARCONVERTER NvEN-roRs: D. J. CAMPBELL BY W. G. WING ATTORNEY Dec. 27,`1949 D. J. CAMPBELL ET AL 2,492,355

SMOOTHING AND DIFFERENTIATING CIRCUIT Filed Dec, 30, 1942 6 Sheets-Sheet3 FIGB SOLUTION INDICATOR DIAL D. J. CAMPBELL ATTORNEY Dec. 27, 1949 D.J. CAMPBELL ET AL 2,492,355

SMOOTHING AND DIFFERENTIATING CIRCUIT Filed Dec. 50, 1942 6 Sheets-Sheet4y L FIG. 4

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`|NvENToRs= D. J. CAMPBELL w G ATTORNEY Dec. 27,1949 D. J. CAMPBELL ErAl.

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SMOTHING AND DIFFERENTIATING CIRCUIT vE5 Sheets-Sheet 6 Filed Dec. 30,1942 inval O N Nmmx AI .2212i l.|| mmm lNVENTORI D. J. CAMPBELL W. G. WlJ Y NG y im ATTORNEY Patented Dec. 27, 1949 UNITED "1;S'fTfEQESIT'LSMOGTHING AND DIFF-ERENTIATING '.JCIRCUIT David .TZCampbell,RichmondHilL anl Willis G. "".WringfWest Hempstead; N. Y.,assignors toThe l"Sperry'-florporationfa. scorporationwof" Dela- 'aware.e Application -December 30,;1942, Serial Nef/10,686

l 4-23"Gla,ims. (015235426115) 'The present invention relatesg,enei"ally, tjo' the may,be assumed constant, andv the other input, art ofdirecting gunfire against amoving target, consisting of a rectilinearcoordinate of present and more particularly, tomeansfor, and methods,.targei. position, may be ,considered as changing of, continuouslycontrolling there of guns so 'at a constant rate. as tol effecthitsagainst rapidly moving targets, 5 ggThe amplitude ratio is ameasure-of the exsuch as airplanes. tent to ,which spuriousperturbations in the pres- Th-e velocity and'directionof'flight of'anytarent position input data are reflected into Ythe get may be'vectoriallyrepresentedby'anyV syspredicted position Aoutput data.Because ofthe temv of threecomponentivelocity vectors"which'impossibility of obtaining-perfect tracking of the are mutually'perpendicular to one anotheriIf 10*V target resulting vfrein backlashrin the gears, and these Vcomponent velocity-Vectorsare"multiplied forother reasons;thepresent-position input data by a time equal to theprojectiletirne' of iiightk to ---contain--srnallmerraticy Variationsfrom the`v true the targets futureposition and then `[combined presentposition of the'target.`- A differentiating vectorially;thepred'ctionthat is; the movement Mandpredictioncircuit which willsubstantially of the targetduring that'timein' the ldirection15"disregardthese Verratic variations and useonly of theresultant=velocityevector isrobtainedf If theaverage' of the inputdata,which average repthe resultant prediction is vectorially combined'-resents 'the )true present position of the target, is withthetargets"-present position, -the'fcorrect -saidto have good smoothingcharacteristics, or

future position`- ofthe-target isf determined. allow-amplitude ratio.Hence, it is clear that two ofthe prime-'functions 20 ffl'olil@lDlllflOOSe OffObtanng a comparison@- oi any director vare4iirst;-to=olotainLA the' corn- 4tween differentiating and predictioncircuits with ponent time derivatives1 of the-targetsemotion, respect.to their smoothing: characteristics, itY is second-"tol multiply-thesecomponentrates assumed that the erratic variationsappear in by a time offlight in order to obtain the correthe form: of Sinexi/aves;superimposed .on the true spending predictions. 25cm-esenteposition-input data. Amplitude ratio Accordingly,'all lapparatus-forthe=so1-ution' of v .maybe delined, as vthe ratio of the amplitude ofthe rire-controli-problernmustnecessarilyinclude :'.fithe sinusoidalperturbations superimposed on the son'ielrind-- of fliierentiatingorfrate measuring h1predicted:.position outputdata to the amplitude vdevice, and 'also fsomef kind:Y of.rnultiplying or `fof;theJsinusoidalperturbations superimposed on prediction device'.inforderJtocontinuouslydeter" 30-z:the/presentipositioninput data, if a liXedperturmine the future position of the target;- ifsince .i lcationfrequency and a constant time oibflight these two devicesfcooperatetozproduce aicomare assumed. monlresultnamely, :aidetermination ofthetar- .szSteady statelag error ina differentiating and gets `futurepositiong'lrthey wille hereinafter. be prediction circuit is a-,measureof the inherent erconsidered together ascconstitutinga unitarygcir-35;.;roru-,which arises; in1 prediction even after,y sufcuit, .referredtoasithe diierentiating and'precientimellaSgelapsedaS. to Anullify alltransient diction circuit. These differentiating-land-preespQnserieIrorsg For the purpose ofcomputadiction:circuits":are'principal:components of any rtiOIl',,steadytatelag;error in a rectilinear Aconi--directonnnandz.criticallyinfluencestheieiectivengponent. @frherill-ltsrmoenmay be definedas ness of the instrument. 40 the error inyards in the rectilinear component The oVer-ailaeiectivenessotanynerentiating i of :prediction which is efiected. by a constantlyand predictionzcircuit;mayloe-determined from ;chang,ngf.time of flightVunderithe conditions of aconsideration#of-ritsrdynamic:icharacteristics, f a specific time offlight and `a constant rate of which consist: o-f the following threeffactors: ...change of present positioninput data if suicient (l)settling time, (2) amplitude ratio, and .(3):-45f.t1me.haselapsedtonullifyI all response errors. steady statelagzerror. f.- ;Presentlyuseddiierentiating andfprvediction The settlingi timev is 'a-measureofihotwmuch 'circuit/s, such as :the .one disclosed in EatentNo.

time the circuit requires to'iadequatelyrespond, 2,085,303entitledvApparatus for the control of that is, to solveforthe'predi-ctedfposition ofzthe .f-.gurlflra issued December 22, 1936, inthe names target. If the director is predicting in a,recti. 50 of E. W.Chafee, H. Murtagh, and S. G,. Myers, linear coordinateesystem, asisi-the'. :director of .eelnployfone variable speedVV device of. theconventhe l present-invention,asettling.time may begegn- .1 tionalvdisc,ball and4 cylinderv type. sidered as the time after which.- all.response er Y The novel,differentiatngand prediction cir- -rorsarenegligible,(lessthan an arbitrary-value). cuit of the.present-,nvenf/OH @m1910575` two Yari- For the purposeotsccmputatiomtirne ofglightf :3.5 ablespeed devices for.di-iierentiating,p andy anin- 3 dependent dead beat multiplier formultiplying, in such a way that the dynamic characteristics of thecircuit are much better than those of any other known predictioncircuit.

The steady state lag error, which arises in the diierentiating andprediction circuit described in the above-mentioned Patent No. 2,065,303from the use of a variable speed device for multiplying is eliminated inthe present invention by performing the multiplication function in adead beat multiplier, which operates independently of thedifferentiating circuit. By a dead beat multiplier is meant one whichinstantaneously solves for the true product of the instantaneous valuesof the two inputs, that is, one which has no inherent lag. The term deadbeat is used in a similar sense throughout this application.

The differentiating and prediction circuit of the present inventiongenerates smooth measures of both the present position input data andthe component rate data, with the result that an amplitude ratio of lessthan unity may be obtained. Thus, it is possible to produce output datawhich is smoother than the input data employed. It can be shown that, bya proper choice of circuit constants, the differentiating and predictioncircuit of the present invention may be caused to have an amplituderatio which is only a small fraction of that of the circuit described inthe aforesaid Patent No. 2,065,303, when the circuit constants are soselected as to -enect a settling time which is substantially equal tothat of the prior patent.

It is also proposed in the differentiating and prediction circuit of thepresent invention to'pro- Vide means for changing one of the circuitconstants during the process of the solution so that a low settling timeis obtained during the time of transient response, and a low amplituderatio will thereafter result. In this way, the circuit will generateaccurate data in a minimum amount f time, and will generate accurate andsmooth data thereafter.

The over-'all effectiveness of any gun director, besides beingcritically aiected by the characteristics of the differentiating andprediction circuit, is also Vinfluenced by the completeness and accuracyof the ballistic solution, and by the accuracy of all the othernecessary operations, such as adding, subtracting, multiplying, torqueam- Y plifying, and solving for a dependent variable through the use ofa cam.

Prior gun directors employ very approximate Wind and drift corrections,and attempt to correct for variations in air density and muzzle It isVtors can be maintained on all cams, and little power need be taken fromthem.

In prior gun directors, such as the one disclosed in copendingapplication Serial No. 434,090

for an Anti-aircraft gun directing system, filed March 10, 1942, nowabandoned, in the names of E. W. Chafee, C. G. Umsted and L. C. Warner,a

4 correction for fuze dead time is eiiected by an operator manuallymatching two dials, one of which is under his control. In the presentinvention automatic means are provided for correcting for fuze dead timewithout the necessity for matching dials.

Prior gun directors have been adapted to operate, if desired, withtarget data received from a radio sight which is located at a distancefrom the director. The present invention incorporates, as an integralpart of the director, a radio sight which may be used instead of theoptical sight, if desired. The target data so obtained is automaticallyset into the director by suitable servo means, thus eliminating errorsarising in the transmission of the data and in the manual matching ofdials which was previously required to set such data into the director.

Accordingly, the principal object of the present invention is to providean improved gun director which will function effectively againstexisting aircraft targets.

Another object of the present invention is to provide a novel gundirector with superior dynamic characteristics.

A further object is to provide a mechanical diiferentiating andprediction circuit in which there exists no steady state lag error.

A still further object of the invention is to provide a mechanicaldifferentiating and prediction circuit which also operates as a veryeiiective smoothing circuit.

An object ofthe invention is to provide a mechanical differentiating andprediction circuit in which the future position data produced may besmoother than the present position data employed. Y

Another object is to provide a mechanicaldifferentiating and predictioncircuit in which the dynamic characteristics may be altered during thecourse of the solution so as to obtain a minimum settling time duringthe time of transient response and a minimum amplitude ratio thereafter.

Another object of the invention is to provide a mechanicaldifferentiating and prediction circuit especially adapted to employtarget data generated by a radio position finding system.

An object of the invention is to provide a gun director whichincorporates a complete ballistic solution.

Another object is to provide a gun ydirector which attains a very highdegree of accuracy through the use of dead beat multipliers and deadbeat torque ampliiiers throughout, and correction cams with good scalefactors, wherever cams are necessary.

A further object is to provide a gun director which incorporates anautomatic correction for fuze dead time.

A still further object of the invention is to provide a'gun directorintegrally incorporating both radio and optical sighting means, andradio means for determining the slant range of the target.

Other objects and advantages will become apparent from thespecification, taken in connection withthe accompanying drawings whereinthe invention is embodied in concrete form.

In the drawings,

Fig. l is a iiat schematic diagram showing the principal components ofthe gun director of the present invention.

Fig. 2 shows aschematic representation of the rectilinear convertersshown in Fig. 1.

encanto Fig. `dis a schematic irepesentatlon oi the mechanical'uiiierntiatmg fatm'eprediction:cire cuit ofthe present invention. f f

i'ifgsllanda dare diagramsfnseiul in exp1aming the theory ofoperation/of the electrical =sys' tem employed inthe'iiseiil'.'inliit'xyiii. "I

Fig. 6 lis awningmagrarnehowingjtne electribal Connections btv'fbclht fthe' und-lrtr Shot'illi if-i ig. "'14 --Fig 7 is 'tt-system of curveswhich-snow lthe eirec'tei.varyingv the constants' ofj'the -rnechaniecaldifferentiating and prediotihgcili'fcuitg-Shovn in Fig. Bl, oni-'thedyianne iaaetenistiesfio'the Fig. e illustrates a niodinoation 'oi-themechanical dilerentitinlg "prediction lclrtiuit, Vshown-i'n-iiig:3,4nWhh one Ijtleci uit"f'cnn= stant'srnay-bernanuaiiy eddiinn process f y:il i, 1; :l A.

Fiese snows a det' i1 er Fig. 8. l Fig. 1o iii-'lustratesia inodinoatienor vthe circutshown'ineFig. 3-finV hi'hb 'iottheCi-rcui't' constants 'isautomat I ered *alluringA v"the courseof the solution. i

Fig. 41'1`i`S arepies'nttbh (if the primary bailistic corrector shownschematicallyY in Fig. l'. L Fig: 12-i"s 'ad representation iif'helSecondary ballistic 'correctorfshownsciiriiatic ly in Fig. 1. Fig; Yi3is -a--iepresentation fof. v.l'ie--ifiize' con verter" and corrector*showin-l" Similar characters oi reference are used in al1 of Y'theabove ngure'sf indicate{correspondingparts. :.,1 ;:...ii.,. The solutionof the nre control proble-rn involvesthree distinct and 'independentur'ictions; '(1) obtaining continuous Jdata representan of the present'position of' thetarg't "hy-tracking fthe target with a suitable;sight;l f2); lempioying#this present position tlataj` in", a-ifferentiaiting 'and prediction "circuit to obtain data representativeof the iuture positionorthe target; la) utilizing the future positiondata'in 'alballistie mechanism to obtain data for positioning thelguns.filata for settingV the ,projeotilefufzejfand ti "e fo'i 'nightdata for tlier prediction "ciifctu't,` I l Referring Jto Fig. i' inwhich one embodiment of thel present inventionis'snown, input snaftsls,351; and 5'4 to'gtnej reotilinearconvefter nare-caused Ato rotateamounts 'creport nai to the present Al'oo'sito'n ot'thetarg'et'! 4a'zunu'th (At), 'elevation (Ee),'and slantyrange (Dt); 'ref specti'vely.In order 'to'accoinplishvthis"result, either automatic `riu'iio'tracking rn'e'anso'r' ual optical tracking'means may'beeinpl Zed, 'as'seleotiveiy determined frein the position o'i the clutch controlhandles Il and 26. K

This Ypresent'position data'gfhating niet been converted to rectangulareoo'rdrna''tesiin.retti-Q4 linear converter l1, i's then set'into' 'thedifferentiating 'and prediction 'circuit' lfwhch'fcrn-J putes the futurevpi'sititjn i" the target. The: differentiating A'and prediction'cir'cuitj' "through electrical "connections, 'not showin nliiif7 '1,causes the motors 1113,' "IDH fand" "IDB', and :consequently the shafts:lill), lill,4 'and 'I'UZSQ I tate 'amounts proportional to theconpted'futu'- 'position o the target in azimuth nepi 'elevation-"intland slant rangeY (De), respectively. i

The future azimuth las) ,'elev'ation :(Ep')` and slantrange 1Ds) data,appearing asiproportional rotatin'so'f shafts lili), '1'01 andillfespectively; are modified in the prinia r""'"'t"o'r tations ofshafts '221, r246,;-anr1 zal .proportional tov angle of train `V(A. To),`orientant"sel'ei'fatlon' (Q. E.) and time of ightt'p'. tithe 'iolflight (tp) signal lis furtherinoi'ed in the'tuze converter andVcorrector 'M9 Vto Aobtain rfuzelsetf-i ting (AF.) data`which'raus'peai-s': as .aproportional' rotation of shaft 252.; Timeofnight (te) then set into the differentiating and prediction-cit' cuit15 and'angle otrain (lA. 'm1, quadrantele- Vation "(Q.' E), and fufs'ttin'g (F) data' are transmitted to the guns' "bytr'a'i-isni''itte'rsr 222;A '2in and 253;' respectively. W

A's previously 4pointed out, the three ln'aoi' functions iin 'thesolution o'f 'the control prne lem, set out in the -abo'i/e paragraphs,fare disltion and ballistic apparatus disclosed.

Referring now to the means ldisch.)'seti in Fig. f1 for obtaining datarepresentative "of the pre n't position of the target, reference numeral`I"de f hates a ''xed azimuth gear lixedly postijone I `n the `supportof the director. The rena'inderbf the apparatus shown 'in'Figfl i's-mountedjrotatf ably with respect to xed vgear `I and' 17o "the directormount, as in prior gunjdirec'tors.

As previously pointedout, -'two modesff opera-l 'tion ror the controlofthejdirec'tor 'in azimuth and elevation 'are provideijopticalfanidradio; as selectively dete'rminedby the jp'osit ofthe clutch` controlhandles and'26 `and"clutches I'U and 21.

' When clutch Ill isin lthe 'opticalpositionmas shown, control ofthe'director infazimuth olotained -from an azimuth control handwl'eel`l. which serves to directly actuate' onev 'memberf wheel 2 alsoaotuates, through ,jgearinfg'lkfrition clutch V5' and gearing 6,"a'.''vari ersl'oe'e'd power device 'l Whose 'output sh'aft48 "isthereb'yvcausedv to rotate-at 'a' 'rate' propo,rtionalV to"y the setting ofazimuth control handwhevel' *2J The variable speeddrive 'l 'maybejoffa'ny'suitable type, as, for example, the conventional disc, Iballand cylinder type vof variablespeed`device,' or a variable 'displacementhydraulic pump andj'inotor unit,kn'own as theVickers unit.' The motions;of -fcontroi".h'andwneel 2 and off the output sh-aft s .of 'variatie.speed drivefi are additively y-jcmnloined in differential '3;'vr/.hosejout`y put shaft` 9 is vtl'rereloy 'driven at 'a .rate-fcorresprondingto the displacement-of control-handle M2.

Withr clutch 'It 'in the mtieai'Y'.,pc'isition( as shown. shaft e isconnected through .clutehmgm and gearing '1'2 to shaft' P9 so astoaetuatethe Worm gearv I3'. 'The Jinter'actionio worm A.gear 153portionfof the'diectortowalk aroundfxed gear 'l land thereby rotateinlazimutn. "There is Vthas obtained 'what' is usually termedfaidedtra-alt4 gff in azimuth. I'f desired,y an azinuth.,rate .contini knop i4'may be employed toctuie the vvariallle speed drive 'l alone, inpwhic'nv`ease .friction eluten .A second Worm gear l5 Vandthe presen-tinput'z'sjh'a'ft, |"6 ,.'a're'lsiniultelllif;.actuated worm'gearirs,Vthus setting' present' 'azimuth (Ad) into the rectilinear converterI 1,and providing a visual indicationv vof present azimuth (Ao) on dial I8.Thus, inthe optical position of vclutch I0, present azimuth (Ao) Vdatais obtained through the manual operation lof handwheel 2 and/or the ratecontrol knob I4, whichare manipulated by the azimuth ,operator so as tomaintain his sight 2| on the target.

' In a similar manner, an elevation control handwheel 22 and anelevation rate control knob 23 are provided for obtaining presentelevation (En) when the clutch control handle'r26 and clutch 21 are `inthe optical position. In this case, elevation control handwheel 22and/or the elevation rate control knob 23 provide a similar type ofaided tracking by means of the variable speed power drive 2B and thedifferential 24, whereby the output shaft 25 of differential 24 isrotated anA amount corresponding to the present elevation of the target,when the target is being tracked in elevation by meansV of thevelevation telescope 28. Y

-Output shaft 25 operates through clutch 21 and gearing 32torsimultaneously actuate shaft 29, worm gear 3B and the presentelevation input shaft 3|. In this'way, present elevation (Eo) is setinto the rectilinear converter I1, and an indication of presentelevation (En) is provided on dial 33. The optical sight 34 and radioscanner 35 are also elevated in accordance with present elevation (En)from shaft 3l 'so as to track with the target, as by gearing 36, 31 and38 an their cooperating shafts.

Thus, in the optical position of clutches IIJ and 21, it is seen thattwo operators, by manual operation of the handwheels 2 and 22, cause thesight 34 and scanner 35 to track with the target, and at the same timeset present azimuth (A) and `present elevation (Eo) into the rectilinearconverter I1.

In the radio position of clutches I0 and 21, the servos 4I and 42,operating under the control of the radio tracking circuit 43,automatically perform this same function. The radio tracking circuit 43,which may be of the type described in copending application Serial No.441,188 for a Radio gun control system, filed April 30, 1942, in thenames of C. G. Holschuh, G. E. White, W. W. Mieher and J. E. Shepherd,is adapted to cooperate with scanner 35 so as to radiate periodic pulsesof electromagnetic energy toward the target and to receive backV fromthe target a reflected portion of this energy. The radio trackingcircuit 43 is also adapted to interpret the varying magnitude of thereceived pulses of electromagnetic energy so as to produce, as on outputleads 44 and 45, direct voltage signals proportional in magnitude andpolarity to the magnitude and sense of the azimuth and elevationtrackingerror, respectively. A v Y. A

In the radio position of clutch I0, the azimuth servo 4I, operatingunderthe control of the azimuth tracking error'signal voltage receivedon lead 44, acts upon shaft I9, through shaft 43, clutch I0 and otherappropriate shafts and gearing to maintain the scanner 35 aligned inazimuth with the true line of sight to the target, and to set presentazimuth (Aq) into the rectilinear converter I1. The azimuth servo 4I maybe of any well-known type adapted to produce on its output der thecontrolof'vthe elevation tracking error signal voltage received on lead45, through shaft 41, clutch 21 and other vappropriate shafts andgearing, to cause the scanner 35 to track with the target inelevatiomand-to set the present elevation (En) into the rectilinearconverter I1.

The third coordinate, slant range V(Dn), necessary to fully determinethe present position of the target, is continuously obtained by radiomeans and automatically set into the rectilinear converter I1, in boththe optical and radio position of clutches Iand 21. y

YFor this purposean automatic range circuit 48 is provided, which may beof the type disclosed in copending application Serial No. 375,373 for aPhase angle indicator, filed'January 22, 1941, now Patent No.'2-,370,692of March 6, 1945, in the name of James E. Shepherd.' As described inthat application, such a circuit, uponH-receiving information on lead..49 'from the radio tracking circuit 43 as to the time delay between theradiation of a pulse of Velectromagnetic energy'and the receipt of the`corresponding reected pulse, is adapted to produce, as on output lead50,a direct voltage which is'proportional to the slant range (D0). i

V'Ihis slant range voltage signal on lead 50 c011- trols the slantVrange servo 5I, which, in this case, should be of the type which isadapted-to produce a rotational displacement of its outputshaft 52proportional to the input voltage signal on lead 50. Output shaft 52,actuates Worm gear -53 and shaft `54, thereby setting slant range (Du)into the rectilinear converter I1, and providing a visual indication ofslant range (Do) on the dial 55`.

The rectilinear converter |51, having been supplied with input. datadeterminative of the present positionof the target in sphericalcoordinates, Ao, Eo, and Dnfon shafts I6, 3|, and 54, respectively, isadapted to convert this data to the corresponding rectangular coordinatedata, x0, -yn and zo, `which then appear as proportional rotations ofthe output shafts 10, 1I, and 60, respectively. Q .A Y

-The rectilinear converter I1, which is shown in Fig. 2, consistsessentially of only two types of components, multiplier units, and sineand cosine units, both of which are Ydead beat mechanical calculators.The multiplier units are preferably of the type described in priorPatent No. 2,194,477 for Multiplying machines, issued March 26, 1940, inthe names of W. L. `Maxson and P YJ. McLaren. As described in.that,patent, suchamultiplier unit is adapted toproduceV a rotationofits output shaft instantaneously equal to orproportional toY the productof the rotations Yof its two input shafts.

The principal element of .the above-mentioned Patent No. 2,194,477 is aspiralgear having teeth mounted thereon in, SllGh a path that a crowngear in contact with these, teeth ,is driven at a speed proportional ,tothasquareof the speed at which the spiral gear. iS `.d1iVen...,'I`1'1esineand cosine units in rectilinearv converter I1 .preferably consist oftwo such spiral gears, the path traced out by the teeth ofeachv of.which is modified such that in onecase, therotationof the driven crowngear is proportionaltothesine of .the rotation of the spiral gear, and'intheother case, Athe rotation of the driven crown gear is .proportionalto the cosine of the rotation ofgthespiralgear. YY`-The Maxson sine andcosine. unit is a well-known device of this character.

Y Referring again to Figi-2, present elevation (Eo) data. is supplied tothe-sine and cosine unit 56, as

l f 9 byishaft f3|. vIliesine and'cosine unitV 56 calcullates sin Eo and'cosEo, and transmits sin En tothe "multiplier unit 59, as 'by shaft 51,and transmits cos Eoto the multiplier unit 6|, as by shaft 58.

Multiplier unit 59, having also received slant :range (Do) as on shaft54, produces, as a propor- :tional rotation of its output shaft-60, thevertical coordinate (zo) of the present target position, which is theproduct Do'sin Eo.

Similarly Vthe horizontal component (Ro) of 1 -slantrange (Do), which isthe product of Do, received on shaft 39, and cos En, received on shaft58,is obtained in multiplier unit 6|, and lis trans- "mitted'to the deadbeat torque amplifier 63 by shaft 62. The torque amplifier 63 maybe ofany 'suitable type adapted to produce, v`as on output shaft 164, atorque amplified signal (Ro) which is "identical to the input signal(Ro) on shaft 62, but forits greater torque. The well-knowntorque"amplifying device, consisting of contacts, a capac-- litance motor anda Lancaster damper, is prefer- "ably used for this; purpose. The torqueamplified f signal (Rc), appearing on shaft 64, is thentransjmittedtothe multiplier units 65 and 66.

Sineand cosine unit k6'?, having received 'present azimuth (Auron shaftI6, calculates sin Ao-and cos Ao, Vand=transmitssin Ao to the multiplier--'unit:65,as on shaft |58,v and transmits cos Ao Yto fthe-multiplierunitz, as on vshaft 69. Multiplier -i unit 65, having received sin Aofrom the sineand cosine unit 61 andRo from the torque amplifier t3,produces, as' a proportional Vrotation of its output shaft'10,`theeast-west coordinate (sco) #of the present position of the target,which is A=the-productY Ro sin Ao. Similarly, multiplier unit 66, havingreceived cos Ao from the sine and cosine vunit 61 andRu from the torqueamplifier 63,1pro- `duces,fas a proportional rotation of its outputvshaft 11|, the north-south coordinate (ya) of the `presentposition ofthe target, which is the product Ru'COSAo. 'W'Thefuncticnsr ofthedifferentiating and prediction circuit 15, shown in Fig. l, are toconvert the received present position data taken withre-:fspectlto'zthedirector, to corresponding present 'positiondata, takenwith respect to the guns; to smooth and differentiate-the resultingpresent A position data; to'compute the future position of -the target;and to control the operation of motors |03,'|04, and |05 such that theshafts |00, AI0 and |02, are rotated amounts proportional to the'fu-:ture position of'the vtarget in terms of future 'azimuth (Ap), futureelevation (Ep), and future `fslant range (Dp), respectively.

The future position data, represented in terms of spherical coordinatesby the rotations of shafts |00, A'|0|,'and 102, are transmitted, as byshafts |25, |26, and "|21, respectively, to the futureposition'rectilinearconverter 99, which then computes the correspondingrectangular coordinates, rcp, yp andra, and transmits this data to theAdifferentiating and'vprediction circuit 15 by shafts |28, |29, :and |30,respectively. Thefuture position rectilinear 'converter 99 may beidentical `to the Apresent position -rectilinear Yconverter '|1, asshownin Fig.` 2.

-The'differentiating and lprediction circuit 15 consists ofthree'identical components, one for each of therectangular coordinates,zc, y and e. Referring to Fig; 3, in which the zr'component of thedifferentiating and prediction circuit 15 is shown, an E-W parallaxhandwheel 'le-is provided -forrsettin'g Vinto the-differential 11, as byshaft -'|'\8,--an input proportional to the distance from lthe gunstothedirector inthe east, or positive x,

direction. This input is additivelycombined in differential 11 with theE-W coordinate (3:0) Yof the present position of the target, receivedoninput shaft 10, to produce on shaft 19 their@` coordinate takenY withrespect to the gunsirather than with respect to the director. Similarhandf wheels 16 and 16 are provided, as shown in lFig. 1, in order'tointroduce N-S and vertical lparallax corrections, into the y and e4components respectively, of the differentiating andprediction circuit15.

As will later be described in detail, the variable vspeed devices 90 and8| operate in conjunction ftionV (PX), which is the product of ('o) s,received onlshaft 84, and' time of flight (tp), received on input shaft86.

The difference differential 89 subtracts V(xos,

y received on shaft 90, from mp, received on input subtracted from thecomputedl prediction '(Px) vshaft |28, and produces the directorprediction '(Pfx) as a proportional rotation of shaft 9|. The

vdirector prediction (PX) on the shaft y9| `isthen on shaft81 in theprediction follow-up differen- -tial 92, the difference, if any exists,Vappearing asa' proportional rotation of output shaft' 93;

The motion of output shaft 93 actuates a`-suit able `contact makingdevice, represented here in simple form as a rack 94, positioned bythepinion *'95, thus'energizing either conductor 91 orvv 98 from conductor96, depending on the direction of rotation of shaft 93. As will be morefully'iex- Apla'ined hereinafter, the selective energiZation-ofconductor 91 or 98 causes a repositioning Av`of 'shafts lIOUQIJI and |02by motors |03, `l0!! Aand A |05 such that the director prediction (PX)eventually becomes equal to the computed prediction (Px), at which-timethedisplacement of -shaft 93" is zero, and neither conductor 91 nor98-fis l energized.

The y and e components of the differentiating and'prediction circuit l5operate identically and simultaneously so that the positions of theshafts l"|00, |0|, and |02 are caused to continuously represent thefuture positionof the targetfas computed by the differentiating andprediction Circuit 15.

Itis obvousthat in order Yto cause PXtobev`come equal to Px, it will bemore effectiveto acvrtuate bne or anotherof 'the three motors |03,

| 01|, and |05 depending on the future position `of thetarget. This isclearly illustrated in Figs. 4 and Y5, Which are a plan view and anelevation view, respectively, of the spatial position of the guns andthe target, in which the guns are reprev`sentedby the -point O, and thefuture position of the target by the point Tp. As there shown,

'the hemisphere may be divided into equal `90" quadrants I, II, III andIV depending on the valuev of Ap. These four quadrants are eachsubdivided into a lower and uppersection depending on'the value of E'p.Thus, the future position of the target Tp, as shown, is 'in quadrantIIL,

-that is, the lower section of the second quadrant. With the futureposition of the'target solocated,

in order to achieve a positive increase in-the :c component oftheffuture position (a positive 1n- Vthe future azimuth shaft |00.V

f crease in PX), it is most effective to drive the slant range (Dp)motor in theY positive direction.

' Likewise, in this case, a positive increase in Py can best be obtainedby a negative increment in AAp and a positive increase in Pz by apositive increment in Ep.

vThe following table summarizes the motor and Y the direction ofrotation of that motori which will be most effective in driving inpositive predictions in the y and c directions when the future positionof the target lies in the quadrant and section indicated.

Rotation Vof the proper motor Vin the correct direction, as indicated inthe above table,'is obtained through the operation of the azimuthquadrant switch |20 and elevation quadrant switch IZI, which are similarin purpose to the quadrant switch described in the aforesaid PatentThese'switches` and their cooperating electrical system are shownschematically 1- in Fig. 6.

The azimuth quadrant switch |20 is shown as consisting of threeidentical four-pole doublethrow switches IIE, I|1 and II8, each ofywhich is indirectly actuated from a single azimuth cam tated accordingto future azimuth (Ap) from As indicated by the direction of the arrow,the cam 400 is rotated vin a clockwise direction as future azimuthincreases and in an opposite direction as future azimuth decreases, onecomplete revolution of the 'cam representing 360 in'future azimuth, so'that for every future azimuth position there is a corresponding positionof the cam, asA indicated by A Thus, the cam, as shown, l is in the zeroazimuth position.

the fixed index 40|.

As cam 400 rotates from its position to its 90 position, the follower402 is displaced upwardly in two successive steps, the first step oc-Switch |I1 is of any well-known type having the characteristic rthat inorder for it lto be thrown in either direction, the control member I I1must be displaced the total distance corresponding'to the sum of the twosuccessive displacements of follower 402. As a result switch II1 willnot throw exactly at the 45 position of cam 400, but rather at a point'slightly past such position in the direction in vwhich the cam isrotating. This delayed action control is a desirable feature in order toprevent rapid transfer of control of the motors, in case .the futureposition (Tp) of the target should oscillate vabout a division linebetween any of the four quadrants. As can readily be seen, cam

It will be understood that the cam 400 is ro- Vtive (rc'ws of mo.

' 400 is'laidY out-in such a way that switch I'I1 is in position I whenthe future position of the target A(Tp) is in quadrants I or IV, and inposition II when the future position of the target isin quadrants II orIII.

Switches I I6 and I I8 are similarly placed under the control of theposition of cam 400-through cam followers 402 and 403 and theirassociated control equipment, which operate identically to the follower402 and Vits associated control equipment.V Thus, switch II6 is inposition I-II in quadrants I or II and in position III-IV in quadrantsIII or IV, and switch I I8 is in position III Vin quadrants II or IIIand in position IV in quadrants I or IV.

The elevation quadrant switch |2| consists of a single four-poledouble-throw switch I I9, identical to switch II1, and a cam 406, whichcam controls the position of switch I I9 according'to the futureelevation (Ep) of the target. vIt will be understood that cam 406 isactuated from the future elevation shaft I0IA such that its position atany time corresponds to the future elevation (Ep) as indicated oppositethe fixed index 40|. SwitchI I9 is placed under the control of theposition of cam 406 through the action of cam follower 401, lever 408and switch control member 409 which 'operate identically to thecorrespondinglequipment in the azimuth quadrant switch I 20. As can beseen, switch |I9 will be in its L positionV in the lower section of eachof the four quadrants and in vits U position in the upper section ofeach of the quadrants.

As shown in Fig.` 6, the terminals |22, |23 and |24 of motors |03, |04and |05, respectively, are

Veach connected'to conductor |01, which is connected to one side of thepower supply. Conductor |06, which is connected to the Vother side ofthe power supply, is connected to the motor terminals |08 or |09, IIO orIII, and II2 or II3, depending on the position of the switches IIB, II1,`I I8, .and I I9 and the contact-making racks 94, 94 and 94" of thedifferentiating and prediction circuit 15.

Energization of terminals |08, ||0 and I I2 from :conductor |06 producesa rotation of the motors I 03, |04 and |05, respectively, in thepositive direction of the corresponding spherical coordinate, whereasenergization of the terminals |09,

III, and I'I3 produces rotation of the respective motors in the negativedirection. As can be seen by tracing the circuits through, the motors|03, I 04, and |05 are thus placed under the control of thedifferentiating and prediction circuit 15 in the desired manner asindicated by the above table.v

Referring back to the differentiating and prev diction circuit 15 shownin Fig. 3, it was previously stated that the two variable speed devicesand 8| operate on the parallax corrected :12u signal, appearing as avproportional rotation of shaft 19, to produce, as a proportionalrotation of shaft 82, a smoothed (ma) s signal in which the spuriousperturbations contained in the :co input signal have been averaged out,and on shaft 83 a rotation proportional to the smoothed time deriva- Themanner in which this is accom'plished will now be described.

The a: component (mo) of the present position, as indicated by theangular position of the shaft 19, is connected'into the equatingdifferential I3I, the output shaft or control member |32 of which ispositioned in accordance with the difference between the rotationaldisplacement of the input shafts 19 and |43. The angular position ofshaft ,|32 represents auseful signal (Sim-as will later `be seen. i'Shaft-1| 32 positions the ballcarriage I 52 which' is vdriven by theconstant speed motori |54,

to the cylinder l|55,in such a way that the rate of rotation of thecylinder |55 is proportional vto the Ydisplacement'of the ball carriage|52 from the center of the disc |53.

The rotation of the cylinder |55l is connected, as by the (cc'o) sshaftt3;r into a seconddiiferential |35, the otherinput of which is suppliedfrom shaft |32 through gearing |33. The output of differential |35,which is the algebraic sum of'its two inputs, actuates-theashaft lM andthe cam |45, the follower or controlmember |38 of which positions theball carriage |38 of a'secon'd variable speed device 80. The cam |46 isso designed that there is just suiicient non-linearity between therotation of the cam |43 and the .resulting displacement of the follower|36, to correct for the inherent slip invariable speed device 80.

Theball carriage |38 of the variable speed delvice 88 variably transmitsthe rotation of the disc |31, which is driven by the constant yspeedmotor |39, to the cylinder |43. The cylinder |43 actuates the (3:0)5shaft |43, which provides the subtractive input to the equatingdifferential |.3|.

In considering vthe operation. of Athecircuit, .it`

will first be assumed that the variable speed device 8|,andthedierential |35 are. omitted,.and that the shaft .HH is directlyactuated from shaft |32. The circuit would then constitute the ordi-'nary"differentiating circuit, which would reach a-condition ofequilibrium when thevballicarriage |38 had assumed such a position'thattheangu- 'lar 'rate of `rotation of shaft A|43 was equal to 'the angularrate ofrotation of Vthe input o shaft i '39. At equilibriumithe vangularpositionrof shaft |41 and cam' vl4li'would'represent the time derivativeof og'srnoothed to a certain extent.

Shaft |43 would beactuated' inY accordancei'with xo, 'also smoothed-to'acertain extent,v but ,it

would lag'zro so that it could not be employed as a source of (1:0)5data.

By incorporating the additional variable speed device 8| in thecircuitgthe lag is automatically removed Yfrom the `(ams shaft |43 sothatits angular displacement is Yan accurate smoothed indication ofthesinput ro. Also, amuch more Veffectively smoothed time derivative('n)s of .the

this time the shaft |32 andV consequently the 'ball carriage|52 of thelvariable speed device 8| will be displaced an amount proportional to thepreviously `mentioned angular displacement :lag of shaft |43 withrespectto shaft 19. Therefore, at this'time theicylinder |55 is stillrotatingand will continue to act through the differential |35 torotateshaft |4|` and thereby further displace the ball carriage |138 ofvariable speed device-8|), with the result Athat the rate Aof rotationof shaft M3 will begin to exceed that of 'shaft 19.

The outputzshaft-|32 of the equating .differential i3!willzthengbeginto.rotate in a direction opposite to its originalArotations() Jas. to drive the ball k carriage 1,152 Yback tothepositionaof Zero displacement. ,Y Therefore, itis kseenthat inlthe noveldifferentiating circuitA iof fthe ypresent :in-

'ventionequilibrium' willonlyfbereached Whenzth'e rate 'offrotation ofshaft :|43 equalsithat offshaft 19; `and when there is no angulardisplacement :lag vbetween the v-two shafts, that when fthe :shaft|32'andithe ball'carriage |52 rhave returned to their zero` displacementpositions.

:shaft 19it'is apparent thatthe angularidispla'cement of the (3:0)5shaft |43 isaproportional to a smoothed. or average mo.

,'Also sincelthe rate of rotation ofV shafts |43'and 'IQfareequal atequilibrium, the angular displace- `mentof shaft `|4| Yisproportional toarsmoothed 'version of. the time derivative of :voiasin the 'ordinarydifferentiating circuit which-*does notincorporate the additionalvariablespeed device 8 "fAt equilibrium, however, it was seen that shaft|32 which provides one input to differential |35 had returned toy` the*position *of zero `displacement, so that the total angulardisplacement'of shaft "-|`4| must have beenproducedfromishaft 83, whichis the otherinputto the differential |35. Therefore', the angularvdisplacement'of :shaft 83: is 4also proportional to a smoothed timederivativelzco) s 0f .'Eo,

Also, since the shaft `83 does not respond to changes in the timederivativeof'o as 'quickly as does the shaft |4|,the:time derivative(x'o)s of .1:0 obtainedas. a Aproportionalrotation of shaft 83 is moreeffectively smoothedithanA lthe'time derivative of .ro which appears asa proportional rotation of shaft MI, and which was obtained in theordinary differentiating circuit employing only one variable speeddevice. Besides :providinga more effectively smoothed (saws signal,shaft 83 also is capable of supplying a greater amount of torque than isthe (rro')s shaft in the ordinary differentiating circuit vwhiclricorresponds-,tosshaft |4| in the present circuit, since shaft 83 isdriven by the constant speed motor |54, whereas the corresponding (o')sshaft in the ordinary differentiating circuit -is driven lfrom theyinput-.m shaft lg'alone.

K T he use of the above described smoothing and differentiating circuitin the-predictionl circuit of the present invention resultsin-'loweramplitude ratios, or in lower Ysettlingtimes for the same amplituderatios, than have previously been obtained.

VThe differentiating and prediction' circuit 2:15, shown in Fig. 3, canbe quantitativelyfanalyzed with respect to its dynamic .characteristicsfrom ak consideration of the "differential equation for the circuit.This equationis foundto beasfollows:

.dzxp l dwp ,xp l @y :1:0 W Ki W+m[ K-T1+KiK2l dt +K1Kz wherein Ki istheproportionality constant for the variable speed .device V30, being.equal to the ratio `of an increment in the angular displacement ofshaft |4| to the resulting increment linthe angular velocity of shaft|43, and K2 is the simllar proportionality constant for the variablespeed device 8|, being equal to the ratio of anincrement in the angulardisplacement of shaft .|.32'to the resulting increment in the angularvelocity ofshaft 83, and p'isthev sum-of Pxfappearing on shaft 8l,and.(o)s,appearing on shaft 98.

In the following we have set forth a derivation of the foregoingdilferential equation, assuming that the circuit comprises'. a: perfectservo and that there is no slip in the variable speed ldrive.

-Itwill be'noted that in Fig. 3 we have illustrated a spiral drum-typecam for moving the ball carriage of the variable speed drive iii) intranslation. The purpose of this cam is to compensate for slip in thevariable speed drive, and, for a perfect, non-slipping variable speeddrive, the lead on the spiral cam would be constant. In deriving theabove differential equation, we will assume either that there is no slipof the variable speed drive or that the cam is correctly calibrated tocompensate therefor.

As illustrated in Fig. 3 and as hereinbefore pointed out, the outputshaft 93 of, differential 92 operates electrical contacts which controla servo motor for driving shaft |28 or putting in the .rp term intodifferential 89. The servo is so controlled that the xp term driven intothe differential thereby is such that If We assume a perfect servo, thenxp can be expressed as g xp= o s+ bostp 2) Forsiznplicity in derivationof this differential equation, let the input be designated by mo; inplace of (ams, let us use x1; and substitute V for the term (rs. Hence,Equation 2 can be Written as follows: Y

,The sensitivityconstant, K2, is defined by the following equation:

The proportionality factor which relates :1:2 and V is necessarily equalto K1 and, therefore, We can write the equation Substituting the valueof m2 from Equation 6 into Equations 4 and 5, respectively, we haveEquation 7 may be transposed to read in terms of :r1 as follows:

and substituting the value of :c1 represented by Equation 9 intoEquation 8 provides us with the equation:

321:30- K 1K 217V When the value of :v1 represented by Equation 9 issubstituted into Equation 3, We obtain the following equation:

Substituting the value of V from Equation 11 into Equation 12 providesus with 1 KlKZ results in the following:

Equation 16, by substituting these values, may be transformed in thefollowing form:

which is the diierential'equation herelnbefore set forth as aquantitative analysis of the circuit shown in Fig. 3.

From a solution of the above differential equation it is possible toplot the curves shown in Fig. 7, from which the settling time in secondsand the amplitude ratio of the circuit may be quantitatively obtainedfor particular values of the circuit constants K1 and K2.

The settling timeV curves are based on a constant rate of change of thea: coordinate of the present position of the target equal to yards persecond, a constant time of night equal to 20 seconds, and a negligibleresponse error in :rp dened as an error of less than '75 yards. Theamplitude ratio curves are based on a constant perturbation frequency ofcycles per second and a constant time of flight equal to 2O seconds. Thesettling times and amplitude ratios are as indicated on the respectivecurves.

As shown, the circuit may have under damped or over damped responsecharacteristics depending on whether values of the circuit constants K1and K2 are chosen so as to be operating above or below the line IBB,each point on which represents a critically damped circuit. The line IBIis the locus of all the points representing the under damped circuits inwhich the first overshoot peak is equal to 75 yards. The settling timecurves are not plotted above this line since, as previously stated, thesettling time curves are based on a negligible response error defined asan error of less than 75 yards.

It would be desirable to alter the dynamic characteristics Vof thecircuit during the solution of the re control problem so as to obtain alow settling time during the time of response and a low amplitude ratiothereafter. From a lconsid.- eration of the curves shown in Fig. 7, itis apparent that this can conveniently be accomplished by a suitablealteration in the circuit constants, such as doubling the constant K2from 3.5 during the time of response to '1.0 thereafter. Thus, with aconstant value of K1, the quick acting circuit, represented by point|52, having a settling time of 8.12 seconds and an amplitude ratio of1.12 may be converted, after the time of response, to the good smoothingcircuit, represented by point |63, having a settling time of 21.1seconds and an amplitude ratio of 0.65. Similar results could beobtained employing various relationships between the initial and finalvalues of the circuit constants K1 and K2. The values indicated areillustrative only, and are not to be construed in a limiting sense.

In Fig. 8 there is shown a modification of the differentiating andprediction circuit shown in Fig. 3 which incorporates manual means fordecreasing the speed of disc |53 of the Variable speed device 8| byhalf, after the period of response, thus doubling the circuit constantK2 and producing the desired improvement in the smoothingcharacteristics of the circuit. Thus, when the circuit constant isincreased by decreasing the speed of disc |53 of the variable speeddevice 8 the sensitivity of said variable speed device is decreased or,in other words, the rapidity with which the variable speed deviceresponds to the input signal and Synchronizes its output to the input isdecreased. Hence, when the sensitivity is so decreased, the smoothingcharacteristics of the circuit are improved.

As shown in Fig. 8, the constant speed motor |55 drives shaft |54 whichsupplies one input to the differential |65, the output of which drivesthe disc |53 of variable speed device 8l as by shaft |18. Shaft |69,which supplies the other input to the differential |65, is also actuatedby the constant speed motor |54, as by shafts |54 and |66, frictionclutch |61, and shaft |68 and the associated gearing, when the smoothingpushbutton |15 is pressed in. In the normal outer position of thepushbutton |15, however, the brake shoe |12 is caused to exert suicientpressure, generated by spring |14, on the brake drum |1| to cause theclutch |51 to slip when shaft |65 attempts to drive shaft |58.

Thus, in the normal outer position of the smoothing pushbutton |15, onlythe input shaft |54 of the differential |65 is driven by the :constantspeed motor |54. However, when the pushbutton is pressed in, both inputshafts |84 and |59 of the differential |55 are driven equally by theconstant speed motor |54, so that the disc |53 is driven at twice therate at which it is driven when the pushbutton is released.

In operation, the pushbutton is maintained in its inner position by theoperator during the time of response of the circuit. It is then allowedto return to its normal position decreasing the speed of the disc |53.by half and doubling the circuit constant K2.

The solution indicator |11, having a visual indicating dial |81 (seeFig. 9), is provided in order to indicate to the operator when thecircuit has reached a condition of equilibrium, that is, when it hasfully responded. Shaft |16, actuated by shaft |32 provides the :csolution indication (Sx) input signal to the solution indicator. Aspreviously explained, the angular displacement of shaft |32, andconsequently of shaft |16, approaches zero as the differentiatingcircuit approaches equilibrium, that is, the vcondition of fullresponse.

The-Sx indicator |18 on the solution indicator dial I8|, shown in Fig.9, is positioned by shaft |16 so that the SX indicator approaches thezero index position |82 as the :c component of the differentiatingcircuit approaches equilibrium. The Sy indicator |19 and Sz indicator|80 are similarly positioned from the corresponding shaft of the y and ecomponents of the differentiating and prediction circuit 15. In this waythe operator is provided with an indication of the duration of theperiod of response, so that he may know when to improve the smoothingcharacteristics of the circuit by releasing the pushbutton |15. Theindices |83 may be used to provide an arbitrarily chosen point in theprocess of response which is considered close enough to the condition ofequilibrium for the release of pushbutton |15. The information providedon the solution indicator dial |8| is also useful as a check on theoperation of the director.

In Fig. l0 there is shown another modication of the `differentiating andprediction circuit shown in Fig. 3, in which the circuit constant K2 isautomatically doubled after the circuit has fully responded. From thedifferential equation for the circuit, it can be shown that the periodof response for the circuit with Xed circuit constants is substantiallyconstant irrespective of the particular problem being solved.

This convenient characteristic is utilized in the apparatus shown inFig. l0 in which a time delay device automatically controls thechangeover to a better smoothing circuit after the constant period ofresponse has elapsed. Thus, the operator initiates the operation of thecircuit by pressing the pushbutton |85. The inward motion of thepushbutton |85 operates a switch (not shown) in the time delay circuit|9|, which switch closes the circuit |86, |81 allowing the battery |88to energize the control solenoid |89. The plunger |88 is thereby pulledwithin the solenoid |89, releasing the brake shoe |12 from the brakedrum |1| and allowing the shaft |68 to rotate and contribute to therotation of disc |53, as before.

The time delay circuit, which may be any of the well-known types, eithermechanical or electrical, automatically maintains the switch within thetime delay circuit |9| in its closed position for the predeterminedconstant period of response of the circuit, after which period itautomatically opens the switch, deenergizing control solenoid |89 andallowing the compression spring |14' to force the shoe |12 against thedrum |1|, thereby preventing rotation of shaft |58 and decreasing theangular velocity of ldisc |53. In this way the circuit constant K2 isautomatically doubled after the circuit has fully responded so as toimprove the smoothing characteristics of the circuit.

It will be understood that in both the manual change-over controlsystem, shown in Figs.

8 and 9, and in the automatic change-over control system, shown in Fig.l0, the shaft |18 also actuates the disc in both the 'J and z componentsof the differentiating and prediction circuit 15 corresponding to thedisc |53 in the :r component shown, so that only one such control systemneed be provided. Accordingly, in the manual system of Figs. 8 and 9,the operator would .release the pushbutton |15 when all three of the 19solution indicators i 18, |19 and |80, corresponding to the solutionindication signals Sx, Sy and Sz," respectively, have settled within thein.- dices`|83.

The third phase of the re control problem involves applying certainmodifications, or ballistic corrections, to the future azimuth (Ap),future elevation (Ep) and future slant range (Dp) data appearing asproportional rotations'of shafts |03, il and |52, respectively, of-Fig.- 1 so `as to obtain angle of train (A. T.), quadrant elevation (Q.E.) and fuze setting (F) for the guns, and time of night (tp) for thedifferentiating and prediction circuit l5.

Thesecorrections can be considered as comprising primary ballisticcorrections, obtained in the primary ballistic corrector |99, which aremadeupof those corrections which exist under standard atmosphericconditions and a standard muzzle Velocity, and secondaryballisticcorrections, obtained in the secondary ballistic corrector 206,which are those corrections necessary to compensate the primaryballistic corrections for variations from standardatmospheric-conditions and from standard muzzle velocity. Both theprimary and secondary ballistic corrections have Yexperimentally beenfound to be functions of future elevation (Ep) and future slant range(Dp).

Referring to Fig. 1, the sequence ofapplication of these corrections soas to obtain angle of train (A. T.) quadrant elevation (Q. E.) fuzesetting (F) and time of flight (tp) Will nowibe considered. The primaryballistic correctorl |99, hav-ingy received future elevation (Ep) andfuture slant range (Dp), as on shafts 250 and 20|, respectively, isadapted, as Will further be described indetail, to produce a rotation ofoutput shaft 262 proportional to the primary super-elevation correction(s)p, and a rotation of output-shaft 203 proportional to the primarytimeof flight correction (Atp).

'The secondary ballistic corrector 206, which will later be describedindetail, receives future azimuth (Ap), future elevation (Ep), andfutureslant rangeY (Dp) on shafts 2|3, 2|2, and 2||, respectively, andv hasset into it percent variation from standard ballistic air density onhands wheel 2i, variation from standardmuzzle velocity on handwheel 203,azimuthal Wind direction on handvvheel 259 and Wind velocity onhandwheel 2li). Having received this data, the secondary ballisticcorrector 205 is adapted to `produce azimuth correction (AA) as aproportional rotation of shaft 2M, secondary. superelevation correction(qms as a proportional rotation of shaft 2|5, and secondary time offlight correction (Atp)s as a proportional rotation of shaft 2|5.

The. azimuth correction (AA) on shaft 2|4 provides one input todifferential 2H, the otherinput being actuated in accordance with futureazimuth (Ap) from shaft 2|8 operating through; differential 2 I9 andshaft 22D. Theoutput shaft 22| of differential 2|? positions the rotorof the angle of train transmitter 22, which, then transe mits angle oftrain (A. T.) to the guns.. An-

angle of train spotting handwheel 223.'. is prop, vided in order toenable the operator tointro.- duce arbitrary spots into the angle oftrain data transmitted to the guns. This arbitrary spot` is obtained bymodifying the rotationk of: the outputl shaft 220 of differential 2|9 bythe rotationof the second input shaft 22,4 resulting; fromoperation ofthe handwheel 223.l

The primaryY superelevationV correction (s)'p, appearing on shaft 2,02,and the-secondary superelevation correction (qms, appearingv on shaft 25, are additively combined in the differential 2i l 4; th e outputshaftoff which is thus rotated an amount proportional to the totalsuperelevation correction (p5). Shaft 239-drives one input member ofdifferential 240, the other input'member of Which is driven inaccordancey with` futureelevationY (Ep) fromvv shaft 24| operatingthrough differential 2,42 and shaft 243. The-outputl spart 246- ofvdifrerentiai 24e positions the rotor of the quadrantelevation,rtransmitter 24J; whichthen transmits quadrant elevation (Q.E.) to vthe guns. A quadrant elevation spotting handwheel 244 isprovided which acts in conjunctionwith shaftk 245 andv differential.242n to allow. arbitrary spots to be introduced into the quadrantemi/ation data transmitted to the guns;

The primary time of ightcorrection. (Atp)p, appearing as aproportionalrotation of shaft203, and the secondary time of iiightcorrectionfntp) s, appearing as a proportional rotation of shaft 216,are additively combined in differential 205120 produceon shafts 228 and229 the-total time of. flight correction (Atp). The torque of shaft 2 29is amplified in the torque amplifier 233. so asto, produce on shaft 235av rotation whichvris also vproportional tothe totaltime ofiiight`correction (Atp), but having a greater torque than doesV shaft 229. Thetorque amplifier 23u-may be identical to the torque amplifier used-inrectilinear Converter Il, or it may-be ofany other si-iitable` dead beattype.

YShaft 235 provides one input to the dierential 23| Whichinput modifiesthe basic slant range (Dp) input received-'on shaft 233, so. as to.produce on output shaft 234a rotation proportional to the time offlight/(tp) Output-shaft 23,4 Aactuates shaft 36 thusprovidingtime ofnight (tp) data for the dierentiatingfand prediction circuit '|5; Shaft2 34 also actuatesshaft 248=1pr0 vidingvtime o-f flight (tp) data-'forthe fuze converter and corrector 24S. Y

Fuze converter and corrector 249, upon also havingA set into it fuzedeadV time (F. D. TJ, as from handwheel 250, is adapted toproduce onshaft 25| a rotation proportional tothe fuzev setting (F), as will laterbe described` in detail. Shaft 25| operates through the-differential2155' to position the shaftv252. AShaft 252 then positions the rotor ofthe fuze transmitter l253 which transmits fuze setting (F) to the guns.The fuze, spotting `handwl'ieel 254, acting in conjunctionwithdifferential 255, provides a means of introducing. arbitrary spots intothe `fuze setting` (F) which is transmitted to thefguns;

The angle of` train, quadrant-elevation, and fuze setting transmitters222, 2141 andl 253, re-

spectively, may be any of the-wellknown types of self-synchronoustransmitters.

Referring no W to Fig. 1l, itisrseen thatithe principal element ofthe-primaryv ballistic-corrector '|99 is a three-dimensional cam-25.5,:the opposite surfaces of Which are respectivelyl usedto obtaintheprimary superelevationcorrection (S)p and the primary time of flightcorrection (Altp)p. Cam 256 is rotated in accordance withfutureelevation (Ep), as by input shaft Zilli` andgearing 251-, and istranslated in accordance withP future slant range (Dp), as `byinputshaft 20.1: and gearing 258.` The-cam is..so designadas to; producedisplacementsnofits follovvers--259z-and 2|| proportional to the,primary superelevation; correction.; (qslp: and, Ythe :primarytime-.:,of night correction (Atp)p, respectively. The lineardisplacement of follower 259 is converted to a proportional rotation ofthe (s)p output shaft 282 as by gearing 268, and the linear displacementof follower 26| is converted to a proportional rotation of the (Atp)poutput shaft 283 as by gearing 262.

Referring now to Fig. l2, in which the Secondary ballistic corrector 286is schematically illustrated, there are shown four three-dimensionalcams 265, 266, 261 and 288, the opposite surfaces of each of which eachprovide one secondary ballistic correction so that the four cams provideeight secondary ballistic corrections in all. The four three-dimensionalcams 265, 266, 261 and 288 are all rotated in accordance with futureelevation (Ep) as by input shaft 212 and gearing 218. The four cams arealso simultaneously translated in accordance with future slant range(Dp), as by input shaft 2l I and gearing 269.

The follower 21| of the upper surface of cam 255 is linearly displacedan amount proportional to the secondary ballistic correction (Atp)a,which should be applied to the primary time of ight correction (Atp)p tocompensate for unit percentage variation from standard ballistic airdensity. The displacement of follower 21| is then multiplied by a factorproportional to the actual percentage variation from standard ballisticair density, as set inby handwheel 281, in the multiplying device 281,so as to produce a linear displacement of the rack element 283proportional to the secondary time of iiight correction (Atp)s necessaryto compensate for the actual percentage variation from standardballistic air density.

Multiplying device 281 is here shown as a linkage multiplying unit,although any other suitable type of multiplying device could be used.The actual percentage'variation from standard ballistic air density isset in by rotation of the handwheel 281, which causes proportionalrotations of the worm gears 212 and 212. The resulting rotation of wormgear 212 produces a proportional linear displacement of the riding gearelement 213. A pin 218 on the riding gear element 213 engages a slot 215in the proportionality element 218, which element is pivoted about thepoint 211. Another pin 218 engages the slot 215 in the proportionalityelement 216, and also engages a slot 28| in the vertical extension 282of the rack element 283, and a slot 219 in the horizontal extension 288of the follower 21|.

In operation, the displacement of the riding gear element 213, producedby rotation of handwheel 281, causes a proportional change in the slopeof proportionality element 216. Since the slope of the proportionalityelement 216 determines the proportionality factor between thedisplacement of follower 21| and rack element 283, the rack element 283is linearly displaced an amount proportional both to the lineardisplacement of follower 21| and to the rotation of handwheel 281.

The linear displacement of rack element 283 is therefore proportional tothe secondary ballistic time of night correction (Atp)a corresponding tothe actual ballistic air density. The linear displacement of rackelement 283 is converted to a corresponding rotational displacement ofshaft 285 as by gearing 284, the rotation of shaft 285 thus representing(Atpha. The ballistic air density referredr to is a fictitiousv airdensity, which takes into account also the temperature of the air, sothat (Atph also compensates for Variations from standard airtemperature.

Similarly, the upper surface of cam) 261 is so designed that the lineardisplacement of follower 288 is proportional to the secondary time offlight correction (Atp) M. v. necessary to compensate for unit variationfrom standard muzzle velocity. The displacement of follower 288 ismultiplied in the linkage multiplying unit 289 by a factor proportionalto the actual variation from standard muzzle Velocity, which is set inby rotation rof the handwheel 288, so as to produce on shaft 298 arotation proportional to (Atphvr. v. necessary to compensate for theactual variation from standard muzzle velocity.

The linear displacement of follower 3|2, which is caused to representthe secondary ballistic correction (Atp)W for unit velocity of rear windby the design of the lower surface of cam 265, is multiplied in thelinkage multiplying unit 383 by a factor proportional to the actual rearwind Velocity (We), which appears as a proportional rotation of thecross-member 388, so as to produce on shaft 3|5 a rotation proportionalto the secondary ballistic correction (Atp)w necessary to compensate forthe actual rear wind velocity.

(Aisha on shaft 285 and (Atp)M.v. on shaft 298 are additively combinedin the differential 288 so as to produce their Sum (Atp)a|-(Atp)1vr v.as a proportional rotation of shaft 292. This sum is then additivelycombined with (Atp)w from shaft 3|5 in differential 329 so as to produceon output shaft 2|6 a rotation proportional to the total secondaryballistic correction (Atp) s necessary to compensate the primaryballistic correction (Atp)p for variations from standard atmosphericconditions and standard muzzle velocity.

The rear wind velocity (WR) and the cross wind Velocity (Wc) areobtained as proportional displacements of the cross-members 388 and 389,respectively, through the operation of the disc and slide mechanism 3|8which receives, as input data, the velocity of the wind (VW) and theazimuthal direction of the wind (AAW) relative to future azimuth (Ap).The disc and slide mechanism 3|8 may be of the same type as is employedin the aforesaid Patent No. 2,065,303 for resolving the polarcoordinates (Ro) and (Ao) of the present position of the target in thehorizontal plane into their corresponding rectilinear coordinates (wn)and (yo).

The lower spiral disc of the disc and slide mechanism 3|8 is rotatedproportionally to the wind velocity (VW), as set in by the handwheel 2|8, through gearing 299. The future azimuth (Ap), received on input shaft2|3, is subtracted in differential 295 from the azimuthal wind direction(AW), as set in by the handwheel 289, and the difference (AAW) isproduced as a proportional rotation of shaft 296. Both the lower spiraldisc and the upper slotted disc of disc and slide mechanism 3|8 areshown schematically as being rotated proportionally to (AAW) from shaft296 through gearing 291.

As is well known, the rack element 385 will then be linearly displacedan amount proportional to the VW cos AAW, or to the cross Wind Velocity(We) and the horizontal element 308 which opcrates into the linkagemultiplying units 383 and 384 will be linearly displaced an amountproportional to VW sin AAW, or to wind velocity (WR) The horizontalelement 383 which operates into the linkage multiplying unit 3H islinearly displaced an amount proportional to the cross wind velocity(We) by the linear displacement of the rack element 385 operatingthrough the gearing 386, shaft 38E and gearing 388.

animano YThefollowers3211, 321|=andt322 are linearlyi displacedzamounts.proportional.. to. the.. secondary ballistic; correction'. (35),@necessary vtov compen. sate.- for. unit 1 percentage variation from'.standard ballistic air. density, to. the.y secondary.' ballisticcorrection (fps) M.v. necessary'to compensatefor unit variation-fromstandard muzzle: velocity and tothe-secondary ballistic correction(39m/:necessary to compensate for unitrear Windzvelo'city, respectively.The linear displacementszof'foh lowers 320,'32I and-'322 arerespectivelymultipliedi in linkage multiplying units 323, 3224and134byfactors proportional to the actualV percentage Variation fromstandard ballistic air density, the actual Variationfrom standard'muzzlevelocity, andthe actualrear.Windvelocity (WR), respectively, so as toproduce'onshafts 325,v 326y and 321 rotations proportional tothesecondary ballistic correction (es), a, the secondary'ballistic correo'-tion` (39M. v., and the secondary-ballistic. correo.- tion ps) w,respectively, corresponding to--theac'- tual conditions of ballistic-air density, muzzle velocity and rear wind Velocity, respectively..

The secondary ballistic corrections Kos), a Vand (4)5) M.v.appearingonshafts 325`and-326, respectively, are additivelycornbinedin differential 328 soas to produce on .shaft 3|9 a rotationproportional to their sum (S),a-|-( S)M.v. This sum is additivelycombined with the secondary ballis tic correction (s)w, appearing onshaft 321, in differential 3|1 so as toproduce on output shaft 22| 5fthe total 'secondary ballistic correction (45s) The lateral deflectioncorrection (5w)- neces-l sary to compensate for unit cross windvelocity(We) is obtained as a linear displacement of the follower 330 of 261.follower 33f'is then multiplied by a factor. proportional to the actualcross wind'velocity (We) in linkage multiplying-unit 3|| sol as'toproduce,- asa proportional rotation of shaft 33|, the true lateraldeflection correction (BW) necessary' tor compensate for the actualcross wind'velocity The driftfcorrection (5D) which is-a lfu-nction'of(Epland (Dp) only, and is, therefore, in reality,

a primary ballistic correction, is produced'las av linear displacementof follower 332-ofcam 238.2' VThe linear'displacement of follower 332 isconverted'to a proportional-rotation of shaft 333, which rotation istherefore also proportional to therdrift correction (5D). The driftcorrection (6D), onvshaft 333,` and the lateral wind deflection (5w)appearing on shaft 33l, areadditively combined in differential 33350 asto produce on output shaft 2|4 a rotation proportional lto the totalazimuth correction (AA).

Thus -it is seen thatthe secondary ballistic corrector2ll6-operates toproduce, as proportional rotations of output shafts 2|4, 2|-5 and 213,respectively,v the vtotal azimuth correctiony (AA), the total secondarysuperelevation correction (ips) s, and the total secondary time ofi'ght'correction (Atp) s.

Referring now to Fig. 13, in which the fuze converter andcorrector 349is shown, one inputof the differential 331 is actuated in accordancewith time of flight (tp) received on shaft 248. Shaft 248 also rotatesthe flatcorrection cam 338, which is so designed that its follower 3331sthen linear.- lydisplaced. an amount proportional tov thecorrection..(Fb-tp) necessary to convert time ofight (tp) into the correspondingballistic. fuze setting (1%)... The -linearrdisplacement offollower.339lis..converted, by gearingfll), to aporrespondingrotationalV displacement offshaftdl,

The linear displacement of whichv is also proportional to the correction(Fb-tp), and'which-provides: the other input. to the differential 331.Thus the-output shaft. 342 of differential 331 iscontinuously'l rotated'an amountzproportional to ballistic.'fuzefsetting"` (Fb) which is thesum of the two. inputs- (tp) and (Flr-tp) to the differential 331.

AsiisLwell known, acertain amount of Ytin'fxeithe fuze-deadtime) elapsesbetween the cuttingof theffuzeand .the .firing of thefprojectile;.andxfuze dead ,time`(F. D. T.)` depending von theprolclency of the-guncr'ew Therefore,1a\dead^ time correo-- tion;(AFD. T.) must be addedto. thexballisticfuze setting..`(Fb) to obtainthe trueffuzefsetting.;(F). Since-Ltheftrue fuze setting) isequalftoswhat the-ballisticfuzesetting. (Ft) lwould be rat'the .time offfring, .that is, afterthezl. D.T. has elapsed, the'correction (AFpp-T.) is.inreaIity-afuzessettingprediction, andthe `problem .can be handledfasfin any predictionsolution.

'The'.fuze settingy prediction circuit is similar Ato that used inpreviously mentionedl priorfPatent No, 2,065,303forobtainingthe:futurevposition of thetarget in the 9:, yandzdirections; Thefball carriage 333 of the Variable speeddevice1344-"isdisplaced. a distance fromtlieV center ofitheedisc 3133 proportional toF. D. T.

asset in by the operation oftheiE; D..T. handw-heel 250. As-the disc-345 of. thevarlable .speed device 344-is drivenY at avconstant-speed bythe constant. speed motor 346, the.V cylinder. 341 is caused to -rotateat -a speed.propoi-tionalto` n L. YF. D. T.

The disc 348 of a second' variable speed 345| device is driven from thecylinder 344fso as to also rotate at a-speed proportional to (cllizs).y

dt of thecylinder35'i'l and. the shaft"342 and in'- versely proportional.to the ratel of rotation (aan) Y i of the-.disc 348.. Therefore, thelinear displacementof ball carriage 353, and consequently the rotationaldisplacement yof shaft..352, is proportional to the product dFb Y ortother required :deadtime.correction-(AFD;'r.-)

The correction (AFD. T. is then. additivelyV courv Y bineclfinthevsecond :differential-.354 with.the-.baL-

25 listic fuze setting (Fb) from shaft 342 so as to produce on theoutput shaft 25| a rotation proportional to the true fuze setting (F).

If desired, a more accurate differentiating and prediction circuit,similar to that shown in Fig. 3 for the determination of mp, could beused in place of the fuze setting prediction circuit shown in Fig. 13.However, it is thought that the accuracy required in obtaining the smallfuze dead time correction (AFD. T.) does not warrant the additionalcomplications involved in the use of the more accurate circuit. Also,the advantages obtained by the use of such a circuit in obtaining :vpare not all applicable to the problem of correcting the ballistic fuzesetting (Fb) for F. D. T. For example, F. D. T. is a constant, whereastime of flight (tp) was continuously varying, so that no steady statelag error can arise in the fuze setting prediction circuit. Also theinput data (Fb) does not contain the erratic variations which werecontained in (me) so that a smoothing of data is not required.

In copending application Serial No, 434,090 for an Anti-aircraft gundirecting system, filed* March 10, 1942, in the names of E. W. Chafee,C. G. Umstead and L. C. Warner, the ballistic fuze setting (Fb) wascorrected for F. D. T. in a similar manner to that described in thepresent invention. However, as described in that application, the ballcarriage corresponding to ball carriage 353 of the present invention hadto be manually positioned by the F. D. T. operator so as to match twodials which were actuated by shafts corresponding to shafts 342 and 335,respectively. It was not possible to use an equating diierential, suchas the differential 350 of the present invention, because the ballisticfuze setting (Fb) shaft, correspondingto shaft 342, was driven from acam follower and consequently did not have sufficient torque to drivethrough an equating differential to position the ball carriage 353.

In the present invention, however, the ballistic fuze setting (Fb) inputshaft 342 is driven substantially from the Dp motor |85, except forsmall correction components of its rotation provided by correction cams,and therefore has suicient torque to allow the automatic correction forfuze dead time, incorporated in the present invention, to be used.

It will be noted that all cams in the present invention are similarlymerely correction cams. In this way, all elements, whose motionrepresents one or another signal, are driven principally from motors,only a small component of the driving force ever being obtained from acam, and therefore these elements all have high torques. Anotheradvantage obtained by the exclusive use of correction cams is that goodscale factors may be maintained on such cams.

It will be understood that the usual friction clutches, limit stops,self-locking couplings, and so forth, which aregenerally incorporated ina director for the protection of equipment and for other incidentalreasons, are to be employed in the present director, wherever necessaryor desirable.

As many changes could be made in the above construction and manyapparently widely different embodiments of this invention could be madewithout departing from the scope thereof, it is intended that all mattercontained in the above description or shown in the accompanying drawingsshall be interpreted as illustrative and not in a limiting sense.

What is claimed is: Y

1. A smoothing and diiferentiating circuit comprising an input memberactuated proportionately to data to be smoothed and differentiated, afirst disc-ball carriage-and-cylinder variable speed device, cam meansfor compensating for the non-linearity in said variable speed device dueto slip, including a cam, and a cam follower driven from said cam andpositioning the ball carriage of said variable speed device, said cambeing so laid out that the rate of rotation of the cylinder of saidvariable speed device is exactly proportional to the displacement ofsaid cam, means for rotating said disc at a constant speed, a controlelement, means for positioning said control element in response to thedifference of the positions of said input member and said cylinder, asecond disc-ball carriage-and-cylinder variable speed device, means forrotating the disc of said second variable speed device at a constantspeed, means for controlling the position of the ball carriage of saidsecond variable speed device from said control element, and means forcontrolling the position of the ball carriage of said rst variable speeddevice in response to the sum of the positions of said control elementand the cylinder of said second variable speed device, whereby thecylinder of said first variable speed device is actuated proportionatelyto a smoothed version of said input data, and the cylinder of saidsecond variable speed device is actuated proportionately to a smoothedversion of the time derivative of said input data.

2. A smoothing and differentiating circuit comprising an input memberand an output member to be Synchronized to the average position of saidinput member, means for driving said output member, a control member forcontrolling the output of said driving means, means for actuating saidcontrol member in accordance with movements of said input, a variablespeed device having a positionable control member and an output member,means for controlling the position of the control member of saidvariable speed device in accordance with the difference between therates of said input and first-mentioned output members, means forfurther actuating said rst mentioned control member in accordance withthe displacement of the output member of said variable speed device, andmeans for varying a sensitivity constant of the circuit.

3. A smoothing and differentiating circuit comprising an input memberand an output member, means for driving said output member, apositionable control for controlling the rate of said driving means,means for differentially positioning said control in accordance with thedifference between the rates of said input and output members, avariable speed device having a positionable control member and an outputmember, means for controlling the position of the control member of saidvariable speed device in accordance with the difference between therates of said input and first-mentioned output members, means forfurther actuating said iirst-mentioned control member in accordance withthe displacement of the output member of said variable speed device, andmeans for varying a sensitivity constant of the circuit.

4. A smoothing and differentiating circuit comprising an input memberand output member, means for driving said output member, a firstpositionable control member for controlling the rate of said drivingmeans, a second control member for positioning said first controlmember,

means forpositioning said second-control member iii-accordance withthe/diierence betweenthe displacement of said input member andthetimeintegral of the movement of saidoutputmember, meansfor positioning saidvrst cont-rol member in accordance ywith the sum of the displacement ofsaid second control member `and the time integral oftheemovement ofsaidfsecond control member, and means for varying asensitivityfconstant-of the circuit. v

Y'5. A smoothing and differentiating: circuit comprising an input memberactuated'proportionately tofdata to be smoothed'and differentiated,Aa'iirst disc-ball carriage-and-cylinderevariable Vspeed device, meansfor yrotating-said discat a constant speed, a control element, means forvpositioning said control elementi in-response to 'the-'difference ofthe speeds of rotation of said'input member and said cylinder, aseconddisc-ball carriage-andcylinder-variable speed device, means Afor4rotating the disc-ofsaid secondevariable speedfdevice at a constantspeed,`means for controlling the position ofthe ball carriage of saidsecondvariable'speed device from said control e1ement,'and means forcontrolling the position-'oftheball carria'ge'of` said rst variablespeed device in'response toithe sum of the displacements of said controlelement nand the cylinder of said second variable speed device, wherebythe cylinder of said rst variable speed device is actuated,proportionately'to a smoothed versionof said input data, and thecylinder of. said second variable speed device isactuatedproportionatelytorasmoothed version of'thetime derivative ofsaid'input dataand.meansjf0r alteringthe speed of `Said disc of saidsecond variable speed device during operation of the circuit, wherebythe `dynamic characteristics Vof the circuit are altered. f

'6. rvA smoothingand differentiating 'circuit comprising an input memberactuated proportionately to data to besmoothed and differentiateda firstdisc-ball .carriage-and-cylinder-variable speed device, means forrotating said disc at a constant speed, a control element, meanstorpositioning said control elementinresponse tothe diierence ofthespeeds Aof rotation of said input member and said cylinder, a ,secondY.disc-#ball carriagefandfcylinder-variable speed device, means` forrotating the disc of said second variable speed device at accnstantspeed,rmeansfor.con trolling the position .of the ball carriagerof saidsecond variable speed device `'from ,said control element, and means forcontrolling the position of the ball carriage of said rst variable speeddevice in :response tothe sum of .thedisplacementsof said .controlelement and the cylinder ,of said second variable speed device, wherebythe cylinder of said rst variable speed deviceis actuatedproportionately to Va smoothed version of said inputdata, andthecylinder of said second variable speed device is actuatedproportionately to a smoothed version of the time derivativeof saidinput data, and means forrautomatically decreasing .the speedof saiddisc-of said second variable speed device at a fixed timeafter theinitiation of response Yof the circuit, whereby the `smoothingcharacteristics of the circuit are thereafter improved.

7. Asmoothing. and diierentiating-.circuit comprising an input memberactuatedrproportionately todata to be smoothed and differentiated, a rstdisc-ball ,carriage-and-cylinder-variable speed device, means forrotating said disc at aconstant speed, .a control element, means forpositioning said control element in response to the difference Z8 ofYthe-speedsof rotation-oflsaid input member and said cylinder, asecondTdisc-ball 'carriage-andcylinder-variable speed device, means vforrotating the disc of-said second variable speed device at a constantspeed, means for controlling the position of the ballcarriage of saidsecond variable speed device from A:said control element, and means forcontrolling the position ofthe ball carriage of -said first `variablespeed device in response to the sum of the displacements of said controlelement'and'thecylinder of `said second variablespeed device, whereby'the cylinder of said iirst variable speed device is actuatedproportionately to 3a `smoothed `version of said input data, Aand the`cylinder of said second variable speed `device is `actuatedproportionately to a smoothed version ofthe 4'time derivative of saidinput data, and means 1for decreasing the speed of said disc of`saidsecond variable speed device during operation of the circuit, and.means for automatically initiating the faction 'of said lastnamed meansvat a ixed time after the initiation of response of the.circuit,-whereby the smoothing characteristics ofthe circuit arethereafter improved.

`8. A smoothing and differentiating circuit comprising an input memberactuated proportionately J15o-datato be smoothedand differentiated,.arst disc-ball carriage-and-cylinderevariable speed device, means forrotating said disc at a constant speed, a control element, means'forrpositioning said controlelementin response to the difference ofthespeedsof rotation of said input member and `said cylinder, a seconddisc-ball carriageand-cylinder-variable speed device, means for rotatingthe disc of said second variable speed device at a constant speed, meansfor controlling the position of `the 'ball carriage of said secondvariable speed vdevice from said control element, and means r,forcontrolling the position of the ball carriage of said first variablespeed device in response to the sum Vof the .displacements of saidcontrol element and the cylinder of Ysaid second variable speed device,whereby the lcylinder of said rst variablespeeddevice is actuatedproportionately to a smoothed version of said input data, and thecylinder of said second variable speed device `actuated proportionatelyto a smoothed version of the time Vderivative ,of -said input data,vmeans for :indicating the deviation of said control element vfrom itszero displacement vp ositiomand means .foraltering the speed of zsaiddisc of .saidsecond variable speed device `during the process y ofsolution, whereby the smoothing characteristics tof the circuit maybevaried fat any desiredindication of said control element.

9. A smoothing and differentiating circuit comprising an inputmember'actuated proportionately to data to be smoothed anddifferentiated, a first variable speedv device having an'actuatingmember and an-output variable rate member, a control element, means forpositioning said control element in response to the difference of thepositions of said linput member and said output variable rate member, asecond variable speed device also having Yan actuating member and anoutput variable ratememberpmeans for controlling the position ofsaid'actuating member of said second variablespeed device from vsaidcontrol element, and means for positioning said actuating member of saidlrst variable speed device in response to the sum o'f the positions ofsaid control element and said output member lof vsaid -second variable

